I love math. It’s the only reason I sometimes wish I’d stayed in school. When I get rich, I want to hire a mathematician to live in my basement and tutor me. I bet they can be had for cheap.
Pure math is potentially a perfect idea. Applied math; not so much. When you see that line of 2′s, how do you know it continues forever? You don’t. You’re making an induction; a beautiful guess. It’s only because you peeked at the real answer—an answer you yourself created—that you can confidently say that you “predicted” the sequence with your method.
I’m much more interested in sequences produced in a simple deterministic way that are extremely difficult to crack. The move from “it makes no sense” to “it’s obvious” is a critical dynamic in human thought. I’d like to see you write about that.
As Polya would say, solving these problems is a heuristic process. The reason you think you find order when you dig down far enough is that you systematically ignore any situation where you don’t find order. Your categories have order built into them. You are drawn to order. There are probably a host of biases influencing that: availability, ontology, instrumentalism, and hindsight among them.
There’s lots of order to be found. There is also infinite amounts of disorder, unprovable order, and alternate plausible order. Occam’s razor helps sort it out—that’s also a heuristic.
I love math. It’s the only reason I sometimes wish I’d stayed in school. When I get rich, I want to hire a mathematician to live in my basement and tutor me. I bet they can be had for cheap.
Pure math is potentially a perfect idea. Applied math; not so much. When you see that line of 2′s, how do you know it continues forever? You don’t. You’re making an induction; a beautiful guess. It’s only because you peeked at the real answer—an answer you yourself created—that you can confidently say that you “predicted” the sequence with your method.
I’m much more interested in sequences produced in a simple deterministic way that are extremely difficult to crack. The move from “it makes no sense” to “it’s obvious” is a critical dynamic in human thought. I’d like to see you write about that.
As Polya would say, solving these problems is a heuristic process. The reason you think you find order when you dig down far enough is that you systematically ignore any situation where you don’t find order. Your categories have order built into them. You are drawn to order. There are probably a host of biases influencing that: availability, ontology, instrumentalism, and hindsight among them.
There’s lots of order to be found. There is also infinite amounts of disorder, unprovable order, and alternate plausible order. Occam’s razor helps sort it out—that’s also a heuristic.